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Conclusion

Alan Weir

in Truth Through Proof: A Formalist Foundation for Mathematics

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199541492
eISBN:
9780191594915
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199541492.003.0010
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter summaries the key thesis of the book: that, given the Sense/Circumstance/World framework in the philosophy of language, we can show that mathematics expresses objective truths, but not ... More


Knowledge by Agreement: The Programme of Communitarian Epistemology

Martin Kusch

Published in print:
2002
Published Online:
January 2005
ISBN:
9780199251223
eISBN:
9780191601767
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0199251223.001.0001
Subject:
Philosophy, Metaphysics/Epistemology

Knowledge by Agreement defends the ideas that knowledge is a social status (like money, or marriage), and that knowledge is primarily the possession of groups rather than individuals. ... More


Proof Set in Concrete

Alan Weir

in Truth Through Proof: A Formalist Foundation for Mathematics

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199541492
eISBN:
9780191594915
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199541492.003.0007
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter attempts to carry out the task promised earlier: a purely concretist syntax and proof theory, where abstract types are replaced by concrete ‘tipes’, construed as fusions of concrete ... More


Avoiding Strict Finitism

Neil Tennant

in The Taming of the True

Published in print:
2002
Published Online:
October 2011
ISBN:
9780199251605
eISBN:
9780191698057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199251605.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This chapter shows how to find an acceptable reading of knowability-in-principle in order to avoid visiting upon oneself and one's opposition the overly restrictive consequence that only the ... More


Quantification and Finitism

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print:
2008
Published Online:
September 2011
ISBN:
9780199550470
eISBN:
9780191701559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550470.003.0004
Subject:
Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

This chapter shows that Ludwig Wittgenstein's philosophy of mathematics has much less in common with intuitionism than is usually assumed, although some strategical moves are barely distinguishable. ... More


From Truth-Functional Logic to a Logic of Equations

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print:
2008
Published Online:
September 2011
ISBN:
9780199550470
eISBN:
9780191701559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550470.003.0005
Subject:
Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

In order to appreciate fully the depth of Ludwig Wittgenstein's commitment to finitism, one ought to look for the causes of his change of mind on quantification. They are to be found in underlying ... More


Strict Finitism

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print:
2008
Published Online:
September 2011
ISBN:
9780199550470
eISBN:
9780191701559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550470.003.0008
Subject:
Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

The philosophical world outside Cambridge discovered the later Ludwig Wittgenstein's philosophy of mathematics with the publication in the 1956 of the Remarks on the Foundations of Mathematics, a ... More


Social Constructivism

Ilkka Niiniluoto

in Critical Scientific Realism

Published in print:
2002
Published Online:
November 2003
ISBN:
9780199251612
eISBN:
9780191598098
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199251614.003.0009
Subject:
Philosophy, Philosophy of Science

Philosophers of science should take seriously the fact, emphasized already by Peirce and Popper, that scientific knowledge is a product of the scientific community. The ontological and ... More


Meaning Finitism

Martin Kusch

in Knowledge by Agreement: The Programme of Communitarian Epistemology

Published in print:
2002
Published Online:
January 2005
ISBN:
9780199251223
eISBN:
9780191601767
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199251223.003.0016
Subject:
Philosophy, Metaphysics/Epistemology

Meaning finitism is a communitarian theory of what it is to master a language. It makes community consensus central in the constitution of normativity. Finitism says that terms have no fixed ... More


Truth

Martin Kusch

in Knowledge by Agreement: The Programme of Communitarian Epistemology

Published in print:
2002
Published Online:
January 2005
ISBN:
9780199251223
eISBN:
9780191601767
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199251223.003.0017
Subject:
Philosophy, Metaphysics/Epistemology

Applies finitism to ’true’ and ’false’. Applying finitism to truth leads to radical and surprising consequences. If ’true’ does not have a fixed extension, then it is simply incoherent to speak of, ... More


Reality

Martin Kusch

in Knowledge by Agreement: The Programme of Communitarian Epistemology

Published in print:
2002
Published Online:
January 2005
ISBN:
9780199251223
eISBN:
9780191601767
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199251223.003.0018
Subject:
Philosophy, Metaphysics/Epistemology

Reviews the contemporary debate between realists (’innocent’, ’external’, ’absolute’, ’metaphysical’) and anti‐realists (’irrealism’, ’internal realism’, ’pluralism’, ’relativistic Kantianism’). ... More


Conclusions

Alexander R. Pruss

in Infinity, Causation, and Paradox

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198810339
eISBN:
9780191847325
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198810339.003.0010
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

The upshot of the preceding nine chapters is briefly summarized and discussed, offering a view of causal finitism as a via media between finitism and infinitism.


Review of Gödel's Collected Works, Vols. IV and V

Paolo Mancosu

in The Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199546534
eISBN:
9780191594939
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199546534.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Mind

This chapter is an essay review of volumes IV and V of Gödel’s Collected Works. Here the aim is to study the heuristics that led to Gödel’s incompleteness theorems by making use of the correspondence ... More


Harvard 1940–1941: Tarski, Carnap, and Quine on a Finitistic Language of Mathematics for Science

Paolo Mancosu

in The Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199546534
eISBN:
9780191594939
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199546534.003.0013
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Mind

Tarski, Carnap and Quine spent the academic year 1940–1941 together at Harvard. In their autobiographies, both Carnap and Quine highlight the importance of the conversations that took place among ... More


The Fluid Dynamics of Political Culture

Stephen Welch

in The Theory of Political Culture

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199553334
eISBN:
9780191756009
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199553334.003.0009
Subject:
Political Science, Political Theory

Chapter 8 accounts for the fluidity of political culture in terms of its discursive dimension. The approach of discursivism has first to be rejected, for it assumes the invariable success of ... More


Infinity, Paradox, and Mathematics

Alexander R. Pruss

in Infinity, Causation, and Paradox

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198810339
eISBN:
9780191847325
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198810339.003.0001
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

Thomson’s Lamp gives a simple example of a paradox of infinity. Different ways of resolving a paradox in general are considered, and in particular two resolutions of Thomson’s Lamp are considered. ... More


The Point of Constructivity

Jan von Plato

in The Great Formal Machinery Works: Theories of Deduction and Computation at the Origins of the Digital Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691174174
eISBN:
9781400885039
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174174.003.0007
Subject:
History, History of Science, Technology, and Medicine

This chapter argues that the best-known statement of finitism is ascribed to Leopold Kronecker (1823–1891). The source of the statement is not Kronecker himself, at least not directly, but rather his ... More


The Finitist Accountant

David Hatherly, David Leung, and Donald MacKenzie

in Living in a Material World: Economic Sociology Meets Science and Technology Studies

Published in print:
2008
Published Online:
August 2013
ISBN:
9780262162524
eISBN:
9780262281607
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262162524.003.0005
Subject:
Society and Culture, Technology and Society

This chapter presents the philosophical roots of finitism, financial reporting in finitist perspective, accounting for economic reality, and rule-governed accounting. Finitism helps people in ... More


Creative Reasoning

John Turri

in Ad Infinitum: New Essays on Epistemological Infinitism

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199609598
eISBN:
9780191779374
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199609598.003.0013
Subject:
Philosophy, Metaphysics/Epistemology

This chapter defends the unpopular view that inference can create justification. The chapter calls this view inferential creationism. Inferential creationism has been favored by infinitists, who ... More


Philosophy of Mathematics

Denis Bonnay

in The Philosophy of Science: A Companion

Published in print:
2018
Published Online:
July 2018
ISBN:
9780190690649
eISBN:
9780190690670
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190690649.003.0010
Subject:
Philosophy, Philosophy of Science

Philosophy of mathematics deals both with ontological issues (what is it that mathematics studies?) and epistemological issues (how is mathematical knowledge possible?). This chapter reviews the main ... More


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